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A single groove in a parallel-plate waveguide (PPWG) has been applied to a tunable terahertz (THz) notch filter with a transverse-electromagnetic (TEM) mode. When the air gap between the metal plates of the PPWG is controlled from 60 to 240 μm using a motor controlled translation stage or a piezo-actuator, the resonant frequency of the notch filter is changed from 1.75 up to 0.62 THz, respectively. Therefore, the measured tunable sensitivity of the notch filter increases to 6.28 GHz/μm. The measured resonant frequencies were found to be in good agreement with the calculation using an effective groove depth. Using a finite-difference time-domain (FDTD) simulation, we also demonstrate that the sensitivity of a THz microfluidic sensor can be increased via a small air gap, a narrow groove width, and a deep groove depth.
©2012 Optical Society of America
1. Introduction
Over the past few years, THz technology has received much attention due to its applicability to the areas of spectroscopy, imaging, and sensing. Numerous passive components, such as waveguides, switches, and filters, are required to complete the development of these systems. Among the passive components, THz filters are very important devices for future applications, including THz communication. Many groups have developed various THz filters using photonic crystal [1–3], plasmonic crystal [4], liquid crystal [5], and waveguides [2,6–9]. Photonic or plasmonic crystals inserted into PPWGs can create a strong THz band gap because most THz fields are concentrated in an air gap between two parallel plates.
The first PPWG used a cylindrical silicon lens that was attached at the input and output of the PPWG to receive and emit a THz beam [10]. The cylindrical silicon lens is the cause of the limitation of the THz beam coupling into the PPWG on account of THz reflection loss from the silicon lens surface. The cylindrical silicon lens has been replaced by a taper or flare structure of the PPWG, which leads to a simplified setup and increased coupling of the THz beam into the PPWG [11]. Moreover, THz notch filters have been demonstrated using slits inserted in the tapered PPWG with TEM mode propagation [7]. The main advantages of the TEM mode compared to the TE1 mode [12,13] are that there are no cutoff frequency and no group velocity dispersion. Because of no cutoff frequency, the resonant frequency of the notch filter can be located along the entire THz bandwidth, which leads to a wider tunable range for the THz notch filter. Another advantage is that the lack of group velocity dispersion can lead to short THz pulse ringing after the main THz pulse in the time domain, which makes it possible to perform a short scan. Recently, THz band gap properties have been studied using multiple grooves inside a flared PPWG [14]. In order to make a THz notch filter using a single groove, the THz band gaps caused by localized standing-wave cavity modes have to be removed. We successfully removed the localized standing-wave cavity modes using a wider and shallow single groove compared to the multiple grooves used in an earlier study (Ref. 14). Moreover the frequency of notch filter was very sensitive according to the air gap variation in the PPWG, leading to a feasibly tunable THz notch filter. In this paper, using the TEM mode, we report the first experimentally demonstrated THz notch filter which is tunable by adjusting the air gap using a piezo-actuator. Therefore, the frequency of the tunable notch can be controlled by adjusting the DC voltage by means of the piezo-actuator. In addition, we report the application of a microfluidic sensor filled with liquid in a single groove that is embedded in the PPWG.
2. Experimental setup
Figure 1 schematically shows the tunable THz notch filter setup, which is composed of a tapered aluminum block and a flat stainless plate with a single groove on the surface. The tapered aluminum block consists of a tapered area with a 3° angle and a flat area. A flat stainless plate, which is the lower part of the PPWG, has dimensions of 50 mm (length), 24 mm (width), and 100 μm (thickness). The single groove, fabricated by a micro-photochemical etching method, is embedded in the flat plate. The single groove is located 6.5 mm from the right edge, which is in the middle of the 13 mm flat surface of the upper plate. Because a vertically polarized (y-direction) THz field propagates to the PPWG, only TM modes exist.
Fig. 1 Schematic diagram of the PPWG. A single groove is embedded into the lower flat plate, which is attached to a piezo-actuator (or a motor-controlled translation stage). (a, b) Optical micrograph of the single groove. Samples A and B show 70 and 105-μm groove widths and 28 and 40-μm groove depths, respectively. (c) Expanded view of the groove.
We prepared two types of single grooves. Sample A has a 70 μm wide and a 28 μm deep groove, and sample B has a 105 μm wide and a 40 μm deep groove, as shown in the image in Fig. 1(a,b). Figure 1(c) shows the definition of the depth and width of the groove. A motor-controlled translation stage is connected to a flat stainless plate to adjust the air gap of the PPWG, and the tapered aluminum plate is fixed. After measuring the notch filter properties, we replaced the motor-controlled translation stage with a piezo-actuator in order to adjust the air gap using a DC voltage source, as shown in Fig. 1.
The THz notch filter can be obtained by inserting a single slit into the middle of the PPWG air gap [7]. The THz notch filter by the single slit can be tuned by adjusting the two air gaps split by the slit. Because the slit is located in the middle of the waveguide air gap, the upper and lower air gaps have to have identical spaces in order to realize the notch filter. This requires a complete experimental setup and a very precise adjustment of both air gaps at the same time. The experimental setup for the single groove, however, provides a much simpler method to make a tunable THz notch filter because there is only one air gap, which can be controlled by one of the PPWG plates. Unlike previous measurements [14, 15], the piezo-actuator used in the experiment here makes it possible to control the air gap by adjusting the DC (or AC) voltage. Also, the groove can contain a liquid that can be applied to a THz microfluidic sensor.
3. Results and discussion
3.1 Data analysis
Figure 2(a) displays the measured THz pulses after propagating through the PPWG with a 100-μm air gap for samples A (upper red) and B (lower black). The images inserted in the THz pulses display the ringing related to the resonance of the notch filter existing after the main pulse. The ringing signal of the sample A has a bigger and longer signal than the sample B. The ringing signal indicates that the sample A has a stronger localized resonance dip and a higher Q factor compared to the sample B. Figure 2(b) to 2(e) show the amplitude spectra of the measured THz pulses with the 100-, 120-, 140-, and 160-μm air gaps, respectively, for samples A (red) and B (black). When the air gaps are increased, the resonance frequencies shift to lower frequency region and also the resonance width gradually becomes narrower. Like the property of the notch filter resonance in the TE1 mode [12], that in the TEM mode is also excellent. The resonant frequencies of samples A and B for 100-μm air gap are 1.29 and 1.13 THz, respectively. Because the groove of sample B is wider and deeper than that of sample A, the resonant frequency exists in a lower frequency range. Unlike the TE1 mode, which has a cutoff frequency, the notch filter resonances of the TEM mode can be obtained for the entire frequency region by adjusting the air gap.
Fig. 2 (a) Measured THz pulses (sample A: upper red, sample B: lower black) for 100-μm air gap. The inserted figures show the expanded THz ringing from 10 to 25 ps. (b)-(e) Spectra of the measured THz pulses for 100-, 120-, 140, and 160-μm air gaps, respectively for samples A (red) and B (black). The inserted figures show expanded images of the resonances.
Figure 3(a) shows the absorbance of the notch filter resonance with different air gaps ranging from 60 to 240 μm. The resonant frequency shifts to a low frequency range and the absorbance becomes small with an increase in the air gap. Because the THz field (energy) in the groove becomes weaker compared to the THz field in the air gap according to increase in the air gap. When the air gap is large enough compared to the groove depth, most of the THz field is distributed into the air gap. Therefore, an out-of-phase (phase mismatch) condition does not (or does only very weakly) arise between the incoming THz field and the reflecting THz field from the bottom of the groove [14,15]. The second resonance of sample B with an air gap of 60 μm is shown to be at 2.09 THz. The second resonance is related to the localized standing-wave cavity mode [14]. When the air gap is wider than the groove width and the groove depth is small enough compared to the groove width, the localized standing-wave cavity mode does not occur, as shown in sample B in Fig. 3(a), with an 80-μm air gap.
Fig. 3 (a) Absorbance spectra in samples A and B when varying the air gaps from 60 to 240-μm. (b) The resonant frequency shift of the notch filters according to the air gaps. The solid lines are numerical fitting lines. Red circles and black squares indicate sample A and B, respectively. (c) Q-factors of the notch filter resonances according to the air gaps.
The resonant frequencies of the notch filter of sample A are 0.62 and 1.75 THz when the air gaps are 240 and 60 μm, respectively. The frequency tuning sensitivity (FTS) is given as Δf/Δg, where Δf is the resonance frequency shift and Δg is the air gap variation. Therefore, the FTS of the THz notch filter is 6.28 GHz/μm, as compared to the value of 1.36 GHz/μm obtained from band gap A shown in Fig. 3(b) of Ref. 14. Figure 3(b) shows the resonant frequency shift according to the difference in the air gap when it ranges from 60 to 240 μm for sample A and from 60 to 320 μm for sample B. The solid lines indicate the numerical fitting lines, which are defined as
where c is the speed of light in a vacuum; g is the air gap; and deff is the effective groove depth, which is defined as (d – Δd(g)). Also, Δd(g) (shown in Fig. 5 (g)) is the height from the groove bottom, which has a very weakly distributed THz field compared to the space above of the groove. Therefore, the height is not considered to determine the effective groove depth. In the fitting process using Eq. (1) in the experimental results, the value of Δd(g) can be obtained using an exponential function, as Δd(g) ≈-M∙exp(-g/N) + y0, where M = 55.51(53.6), N = 83.5(134.5), and y0 = 29.3(34.8) for sample A(B). If the air gap is smaller around 60 μm, Δd(g) approaches zero. This occurs because, in this case, the groove widths are large enough compared to the air gap, which is smaller than the depth, and because the strong THz field in the groove is fully distributed at the bottom of the groove. Therefore, the entire groove depth contributes to the realization of the effective height (heff = deff + g ≈d + g), where Δd(g) ≈0 and deff ≈d. Meanwhile, when the air gap is large enough compared to the groove depth, most of the strong THz field is distributed into the air gap; however, the THz field in the groove is very weak. For this reason, the effective height is only the air gap (heff ≈g), where Δd(g) ≈d and deff ≈0. According to our calculation, the value of Δd(g) can be obtained by an exponential function. The groove depth is the important factor in determining the resonant frequency of small air gap; however, it is less important with a large air gap. For example, when the air gap is 60 μm, the effective depths of sample A (deff = 25.8 μm, where Δd(g) = 2.2 μm) and B (deff = 39.5 μm, where Δd(g) = 0.5 μm) have ratios of about 30.1% and 39.7%, respectively, to the total heights (d + g). The resonant frequencies of sample A and B are 1.75 and 1.51 THz, respectively. On the other hand, according to the increase in the air gap, the resonant frequencies of both notch filters are nearly identical, as shown in Fig. 3(b). For example, when the air gap is 240 μm, the effective depth of sample A (deff = 1.8 μm, where Δd(g) = 26.2 μm) and B (deff = 14.2 μm, where Δd(g) = 25.8 μm) have ratios of 0.7% and 5.6%, respectively, to the total height (d + g). The resonant frequencies of sample A and B are 0.62 and 0.59 THz, respectively. Figure 3(c) shows the relationship between the air gap and the Q factor, which increases with an increase in the air gap. Sample A has a greater Q factor than sample B because it has a smaller groove depth. The maximum Q factors of sample A and B reach about 128 and 69, respectively, which can be compared to the value of 138 as obtained with the single slit in the PPWG [7].3.2 Tunable notch filter using piezo-actuator
Because the weight of the flat stainless plate is only 0.95 g, the piezo-actuator can support the plate. Instead of mechanical movement by the motor-controlled translation stage, the piezo-actuator makes its length longer and shorter by controlling the DC (or AC) voltage supplied to the piezo-actuator. Therefore, the motor-controlled translation stage is replaced by the piezo-actuator, which is 30-mm long (Piezomechanik, model No. PSt-HD 200/7x7/40), as shown in Fig. 1. Figure 4 shows the notch filter resonance variations (red squares) and air gap variations (black circles) of sample B according to the DC voltage supply. Due to the limited length of the piezo-actuator, it increases to 61 μm when the voltage changes from −50 to + 200 V which corresponds to an air gap from 136 to 75 μm. The resonance variation of the notch filter ranges from 0.92 THz (g = 136 μm) to 1.34 THz (g = 75 μm), which is in very good agreement with the data shown in Fig. 3(b). The frequency-tuning sensitivity by voltage variation (FTSV) is given as Δf/ΔV, where ΔV is the voltage variation. The calculated FTSV throughout the entire range of voltage variation is 1.67 GHz/V, which shows that the piezo-actuator can be used with a tunable notch filter device. Because most piezo-actuators have hysteresis characteristics, they require additional controlling equipment to set the position and to control the velocity.
Fig. 4 Measured voltage-dependent resonant frequencies of the notch filter (red squares) and the air gaps of the PPWG (black circles) when one end of the piezo-actuator is attached to the flat plate.
3.3 FDTD simulation
To determine the directional energy flux density of a THz field, Poynting vectors are used, as shown in Fig. 5 ; these show the FDTD simulations considered with a resonant frequency of 1.29 THz, a groove depth of 28 μm (sample A), and an air gap of 100 μm. Each figure shows a 1/12 time period of T, which is equal to 1/wavelength. The figure shows only six frames, which make up a half period of T. After finishing the half period of T, the Poynting vectors repeat the cycle from Figs. 5(a) to 5(f) with an E-field phase shift of 180°. The two opposite directions of the Poynting vectors oscillate in the space between the groove and the air gap of the PPWG. In this case, the THz field is not fully distributed on the groove bottom as shown in Fig. 5(g). Therefore the effective groove depth (deff) is introduced to define the Eq. (1). The energy flux density is confined in the effective groove depth (space) and the air gap. The energy density of the other frequencies moves to the output-side PPWG; however, only the energy density of the notch filter frequency is unable to go to the output-side PPWG. This situation makes the notch filter resonate at the measured THz bandwidth. The process of building up the notch filter resonance by the single groove is identical to that of the single slit measurement [15]; the only difference is the THz field reflection by the groove bottom and the THz field passing through the slit. When the THz fields are reflected from the metal waveguide surface or the groove bottom, which are considered as perfect conductors in the THz frequency region, the images of the THz fields exist inside the metal. According to image theory, the THz field pattern in the groove waveguide is identical to that in the folded THz field halfway along the horizontal center of the slit [14,15]. Therefore, the formation of notch filter resonance by the single groove can be explained in terms of the resonance of the single slit [15].
Fig. 5 Poynting vectors around the groove (sample A) for an air gap of 100 μm and a resonant frequency of 1.29 THz. (a)-(f) Each frame shows a 1/12 time period. (g) An enlarged graph of (d) in which Δd is 12.5 μm for an air gap of 100 μm.
3.4 Application for THz microfluidic sensor
The THz microfluidic sensor is one example of applying the notch filter resonance [13]. Using FDTD simulation, we attempted to calculate the resonance shift for liquid samples that had different reflective indexes ranging from 1.35 to 1.43 based on liquid alkanes [16]. Figure 6(a) shows the variation of the resonant frequency for four different fluid levels in the groove of sample A with a 100 μm air gap. If the liquid level is increased, the sensitivity of the resonant frequency is also increased. When the groove is fully filled with the liquid, the resonant frequency deviation (Δf) is 16 GHz between the reflective indexes of 1.35 and 1.43. The sensitivity is Δf/Δn = 162.5 GHz/RIU, where RIU is the refractive index unit. The groove depth, the groove width, and the air gap are important factors when seeking to increase the sensitivity, as shown in Fig. 6(b). For example, if the groove width and the groove depth are changed to 35 μm (50% decrease; blue line) and 42 μm (50% increase; black line), respectively, the sensitivity levels increase to 255 GHz/RIU and 360 GHz/RIU. When both the width and the depth are changed (yellow line), the sensitivity is increased to 420 GHz/RIU. In this case, if the air gap is reduced from 100 to 50 μm (red line, Δf = 52 GHz), the sensitivity increases to 650 GHz/RIU, which is an increase of four times compared to the ordinary sample condition (green line). This simulation shows that, as in the TE mode, in the TEM mode it is possible to fabricate a THz microfluidic sensor. The advantages of this development are detailed in the introduction.
Fig. 6 (a) The resonant frequencies of the notch filter for four different fluid levels with different reflective indexes. (b) The resonant frequency shift for different sample conditions when the groove is fully filled with liquid.
4. Summary and conclusions
We demonstrate a tunable THz notch filter and a THz microfluidic sensor using a wider and relatively shallow single groove in a PPWG in the TEM mode. When the air gap was controlled within the range of 60 to 240 μm for sample A and 60 to 320 μm for sample B by a motor-controlled translation stage or a piezo-actuator, the resonant frequency of sample A (B) changes from 1.75 (1.5) to 0.62 (0.45) THz. Therefore, the tunable sensitivity of the single-notch filter is approached to 6.28 GHz/μm (4.03 GHz/μm). The measured resonant frequencies of the notch filters were found to agree well with the calculations used to determine the effective groove depth. We show that the THz microfluidic sensor is a good example of the application of a notch filter using a single groove in the TEM mode. A very sensitive microfluidic sensor can be designed using the PPWG setup with a small air gap, a narrow groove width, and a deep groove depth.
Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2008-0062257 and No. 2010-0009070), and was supported by the Grant of the Korean Health Technology R&D Project; Ministry for Health, Welfare & Family Affairs of Korea (A101954).
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